Abstract: With the development of the large scale numerical simulation,computational fluid dynamics and computational solid mechanics couplesimulation becomes the powerful accurate tool in engineering analysis. Butthe large computation cost postpones its widely application in design.Reduced order model (ROM) for unsteady flow field, with good accuracy, loworder and high efficiency, gives an opportunity to CFD/CSD couple simulationin practical design. Based on the description of model reduction theory andmethod in the view of mathematics, the advances of the reduced order modelsfor unsteady flow field were systematically introduced. The systemidentification based ROM such as Volterra/ROM, ARMA/ROM, Surrogate ROM, andflow eigen mode based ROM such as POD/ROM, HB/ROM, ND/ROM were reviewed. Theadvantages and drawbacks were analyzed with the possible direction of theirimprovements. The trends and prospects of the ROM for unsteady flow fieldwere discussed, with the indication that the next generation ROM will bemore robust and adaptive.